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A134939 Numerator of the expected number of random moves in Tower of Hanoi problem with n disks starting on peg 1 and ending on peg 3. 3
0, 2, 64, 1274, 21760, 348722, 5422144, 83000234, 1259729920, 19027002722, 286576949824, 4309163074394, 64731832372480, 971825991711122, 14585021567101504, 218843984372767754, 3283277591489597440, 49254723695591689922, 738870890792896773184, 11083513664870504400314 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Both allowable transitions out of any of the three special states in which all the disks are on one of the pegs have probability 1/2 and each of the three allowable transitions out of any of the other 3^n - 3 states have probability 1/3.
LINKS
M. A. Alekseyev and T. Berger, Solving the Tower of Hanoi with Random Moves. In: J. Beineke, J. Rosenhouse (eds.) The Mathematics of Various Entertaining Subjects: Research in Recreational Math, Princeton University Press, 2016, pp. 65-79. ISBN 978-0-691-16403-8
FORMULA
a(n) = numerator(e(n)) with e(n) = (3^n-1)*(5^n-3^n) / (2*3^(n-1)), a(n) = (3^n-1)*(5^n-3^n) / 2. - Max Alekseyev, Feb 04 2008
G.f.: -2*x*(45*x^2-1) / ((3*x-1)*(5*x-1)*(9*x-1)*(15*x-1)). - Colin Barker, Dec 26 2012
EXAMPLE
The values of e(0), ..., e(4), e(5) are 0, 2, 64/3, 1274/9, 21760/27, 348722/81.
CROSSREFS
Sequence in context: A299724 A047707 A223121 * A217268 A122603 A127691
KEYWORD
nonn,frac,easy
AUTHOR
Toby Berger (tb6n(AT)virginia.edu), Jan 23 2008
EXTENSIONS
Values of e(5) onwards and general formula found by Max Alekseyev, Feb 02 2008, Feb 04 2008
Shorter name by Michel Marcus, Dec 27 2012
STATUS
approved

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Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)